Padovan numbers which are concatenations of three repdigits

Kisan Bhoi; Prasanta Kumar Ray

Padovan numbers which are concatenations of three repdigits

Number Theory 2022-12-22 v1

Authors: Kisan Bhoi , Prasanta Kumar Ray

Abstract

Padovan sequence is a ternary recurrent sequence defined by the recurrence relation $P_{n+3}=P_{n+1}+P_{n}$ with initial terms $P_{0}=P_{1}=P_{2}=1.$ In this study it is shown that $114,151,200,265,351,465,616,816,3329,4410,7739,922111$ are the only Padovan numbers which are concatenations of three repdigits.

Keywords

padovan numbers repdigits concatenation recurrent sequence diophantine problem

Cite

@article{arxiv.2212.10831,
  title  = {Padovan numbers which are concatenations of three repdigits},
  author = {Kisan Bhoi and Prasanta Kumar Ray},
  journal= {arXiv preprint arXiv:2212.10831},
  year   = {2022}
}

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12 pages

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